Abstract
The optimal nearly-analytic discrete (ONAD) method is a new numerical method developed in recent years for solving the wave equation. Compared with other methods, such as popularly-used finite-difference methods, the ONAD method can effectively suppress the numerical dispersion when coarse grids are used. In this paper, the ONAD method is extended to solve the 2-dimensional SH-wave equation in the spherical coordinates. To investigate the accuracy and the efficiency of the ONAD method, we compare the numerical results calculated by the ONAD method and other methods for both the homogeneous model and the inhomogeneous IASP91 model. The comparisons indicate that the ONAD method for solving the SH-wave equation in the spherical coordinates has the advantages of less numerical dispersion, small memory requirement for computer codes, and fast calculation. As an application, we use the ONAD method to simulate the SH-wave propagating between the Earth’s surface and the core-mantle boundary (CMB). Meanwhile, we investigate the SH-wave propagating in the mantle through analyzing the wave-field snapshots in different times and synthetic seismograms.
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References
Igel H, Weber M. SH-wave propagation in the whole mantle using high-order finite differences. Geophys Res Lett, 1995, 22: 731–734
Chaljub E, Tarantola A. Sensitivity of SS precursors to topography on the upper-mantle 660-km discontinuity. Geophys Res Lett, 1997, 24: 2613–2616
Igel H, Weber M. P-SV wave propagation in the Earth’s mantle using finite-differences: Application to heterogeneous lowermost mantle structure. Geophys Res Lett, 1996, 23: 415–418
Nissen-Mayer T, Fournier A, Dahlen F A. A 2-D spectral-element method for computing spherical-earth seismograms. I. Moment-tensor source. Geophys J Int, 2007, 168: 1093–1097
Yang D H, Teng J W, Zhang Z J, et al. A nearly-analytic discrete method for acoustic and elastic wave equations in anisotropic media. Bull Seism Soc Am, 2003, 93: 882–890
Alterman Z, Aboudi J, Karal F C. Pulse propagation in a laterally heterogeneous solid elastic sphere. Geophys J R Astronom Soc, 1970, 21: 243–260
Dablain M. The application of high-order differencing to the scalar wave equation. Geophysics, 1986, 51: 54–66
Graves R W. Simulating seismic wave propagation in 3D elastic media using staggered-grid finite differences. Bull Seism Soc Am, 1996, 86: 1091–1106
Yang D H, Lu M, Wu R S, et al. An optimal nearly-analytic discrete method for 2D acoustic and elastic wave equations. Bull Seism Soc Am, 2004, 94: 1982–1992
Yang D H, Peng J M, Lu M, et al. Optimal nearly-analytic discrete approximation to the scalar wave equation. Bull Seism Soc Am, 2006, 96: 1114–1130
Lapwood E R, Usami T. Free Oscillations of the Earth. Cambridge: Cambridge University Press, 1981
Kenneth B L N, Engdahl E R. Traveltimes for global earthquake location and phase identification. Geophys J Int, 1991, 105: 429–465
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Li, X., Yang, D. & Tong, P. The ONAD method for solving the SH-wave equation and simulation of the SH-wave propagation in the Earth’s mantle. Sci. China Earth Sci. 56, 913–921 (2013). https://doi.org/10.1007/s11430-012-4529-6
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DOI: https://doi.org/10.1007/s11430-012-4529-6